I would like to close summarizing the distinctions in regards to the different types of necessities pertaining to salvation in regards to Baptism, dying within the Church, and supernatural Faith regarding the need to believe in (1) God and that (2) God rewards the good and punishes evil, (3) the Incarnation and (4) the Holy Trinity and whether only the first two or all four are necessary beliefs for salvation to be possible as taught by the Church thusly:
Some theologians teach that two truths must be believed with a necessity of means and others teach that four must be believed. Still others teach that four are only required in places where the Gospel has been preached but only two are required in other places. It all depends on how God willed it. He could have willed to require explicit faith in all four truths or only in two, but in either case He will infallibly grant to each soul the opportunity to arrive at explicit faith in these 2 or 4 truths as the case may be. In the Old Testament, clearly explicit faith in the Trinity was not required.
As far as what is intrinsically necessary, this has nothing to do with the question on whether 2 or 4 truths are required to be believed with explicit faith. Intrinsic necessity would apply to whatever truths were so basic that faith would be impossible without them. For example, one clearly cannot have any virtue of faith whatsoever if he did not even believe that God exists, since faith is a firm assent of the intellect to the truths revealed by God. How could one accept a truth revealed by a God whom he denies exists?
The necessity of believing all 4 truths may still be by necessity of means even though not through intrinsic necessity. Baptism is a necessary means of salvation, but it is a relative necessity, i.e. it is a necessary means because God has willed it to be so; it is a means -- not merely a precept -- but a means because willed by God as a means. However, it is not intrinsically necessary so that God could never grant salvation without it. He can make exceptions to His own plan of salvation, i.e. to the ordinary means: Baptism. Similarly, Mary is necessary for our salvation as a necessary means of obtaining grace, but this is a relative necessity, i.e. she is a necessary means of getting to heaven because God has willed it to be so. Her intercession is not intrinsically or absolutely necessary as St. Louis de Montfort explains in True Devotion. However, God makes no exception to the need for Mary's intercession to get to Heaven; He does make exception to the need for Baptism, and possibly He makes exception to the need to know the Trinity (if we follow the opinion of some theologians).
Also, in another opinion, as pointed out in the quote by St. Alphonsus, some theologians apparently regard belief in the Trinity as a precept and not a means of salvation.
The closest the Church has ever come to answering whether all four beliefs were necessary was in the reply of a Roman Congregation that said one cannot baptize even a dying person without first instructing them
in all four truths. However, theologians agree that this reply was not a definitive answer to the debate but only a
norm for practice.
Obviously it is intrinsically or absolutely necessary to die within the Church for salvation to be possible as we have been stating throughout this series.
Further in order to respond to the Feeneyites objection that we can ignore a letter from the holy office because it is not infallible, to reiterate once again that the minimum amount of articles necessary for one to have the supernatural Faith necessary for salvation to be possible, and whether Jews, Muslims and pagans can be saved I answer as follows:
The "authority" who accepts Suprema Haec Sacra included everyone in the Catholic Church at the time except for Fr. Feeney and his followers - Fenton, for example, certainly accepted it, and why shouldn't he? It was a letter from the Holy Office, whose head is the Pope, and Pius XII himself approved the explanation given. All Catholics are obliged to accept authoritative docuмents, which the letter certainly is, with an interior ascent. To refuse to believe it would be a mortal sin. Further the entire letter is laced with infallible teachings from beginning begging to end in its doctrinal section. For instance the letter teaches that their is no salvation outside the Church. Would the Feeneyites have us reject this teaching because it is "not infallible"?
The question is whether it is possible for Jews, Muslims, and pagans to possess the virtue of Faith. I do not see how it is possible, but from what I recall Bishop Sanborn saying, this was something that was
still being disputed among theologians (emphasis mine), at least as far as the details. Please read Fr. Riccardo Lombardi, "The Salvation of the Unbeliever" (1956) and Fr. Maurice Emynian, "The Theology of Salvation" (1960), for a deeper understanding of this issue. Oftentimes these questions are quite thorny and not so easily resolved. There is a reason why the Church commissions specially trained theologians and not just anyone to tackle such questions.
The Suprema Haec Sacra does not say that Jews, Muslims, or pagans can be saved. On the contrary, it suggests that they cannot, inasmuch as it says that supernatural Faith is required for an implicit desire for baptism.
There is NO question that the virtue of Faith is necessary by an absolute i.e. intrinsic necessity of means. That is indisputable.
Lay people are quite welcome to study the distinctions (and we barely touched on a few of the numerous distinctions and vast amount of terminology pertaining to theology) pointed out at the beginning of this article (but not listed in this post) but should not come to conclusions on issues that have not been settled by the Church such as whether there are two or four minimal beliefs we must have in order to have supernatural Faith.
Saint Thomas Aquinas speaks of the need for belief in the Incarnation and the Holy Trinity:
But when dealing with Baptism of [desire] the Spirit he speaks thusly:
In like manner a man receives the effect of Baptism by the power of the Holy Ghost, not only without Baptism of Water, but also without Baptism of Blood: forasmuch as his heart is moved by the Holy Ghost to believe in and love God and to repent of his sins: wherefore this is also called Baptism of Repentance.
The virtue of humility can off-set head-strong people who insist on their opinions above that of the approved theologians, Fathers, Doctors, Saints and Popes. For it is better to trust what a valid Pope teaches than to trust more in our own intellects:
Certainly we must hold it as of faith that no one can be saved outside the apostolic Roman Church, that this is the only Ark of salvation, and that the one who does not enter it is going to perish in the deluge. But, nevertheless, we must likewise hold it as certain that those who labor in ignorance of the true religion, if that [ignorance] be invincible, will never be charged with any guilt on this account before the eyes of the Lord. Now, who is there who would arrogate to himself the power to indicate the extent of such [invincible] ignorance according to the nature and the variety of peoples, regions, talents, and so many other things? For really when, loosed from these bodily bonds, we see God as He is, we shall certainly understand with what intimate and beautiful a connection the divine mercy and justice are joined together. But, while we live on earth, weighed down by this mortal body that darkens the mind, let us hold most firmly, from Catholic doctrine, that there is one God, one faith, one baptism. It is wrong to push our inquiries further than this. (Pius IX Singulari Quadum)